1
IAT (IISER) 2020
MCQ (Single Correct Answer)
+4
-1
If S is the set of all points $(x, y)$ satisfying the equation $\sin x=\cos y$, then which of the following statements is correct?
A
$S$ contains all points of a parabola.
B
$S$ contains all points of a circle.
C
$S$ contains all points of a hyperbola.
D
$S$ contains all points of a straight line.
2
IAT (IISER) 2020
MCQ (Single Correct Answer)
+4
-1
If $A=\left[\begin{array}{lll}1 & a & 0 \\ 0 & 1 & b \\ 0 & 0 & 1\end{array}\right]$, then the determinant of $I-A+A^2-A^3+A^4-\cdots+A^{2020}$ is
A
2020
B
$a^{2020}-b a^{2019}+\cdots-b^{2019} a+b^{2020}$
C
$2020^3$
D
1
3
IAT (IISER) 2020
MCQ (Single Correct Answer)
+4
-1
Let $S=\{(a, b): a, b \in Q\}$ and $\ell$ be the line $y=m x+c$. Which of the following statements is not correct?
A
If $\ell$ passes through two points of $S$, then $m$ must be rational.
B
If $m$ is rational and $c$ is irrational, then $\ell$ passes through at least one point of $S$.
C
If $\ell$ passes through exactly one point of $S$, then $m$ must be irrational.
D
If $m$ is irrational and $c$ is rational, then $\ell$ passes through exactly one point of $S$.
4
IAT (IISER) 2020
MCQ (Single Correct Answer)
+4
-1

If $p(t)=\frac{t(t-1) \cdots(t-2019)}{2019!}$, then the value of

$$ \int_0^1\left(\frac{1}{t+1}+\frac{1}{t+2}+\cdots+\frac{1}{t+2020}\right) p(-t-1) d t $$

is:

A
$2019^2$
B
2019
C
$2020^2$
D
2020
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